Parallel computing apparatus, compiling apparatus, and parallel processing method

ABSTRACT

A parallel computing apparatus includes a first processor that executes a first thread, a second processor that executes a second thread, and a memory. The memory includes a first private area that corresponds to the first thread, a second private area that corresponds to the second thread, and a shared area. The first processor stores first data in the first private area and stores address information that enables access to the first data in the shared area. The second processor stores second data in the second private area, accesses the first data based on the address information, and generates third data based on the first and second data.

CROSS-REFERENCE TO RELATED APPLICATION

This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2015-113657, filed on Jun. 4, 2015, the entire contents of which are incorporated herein by reference.

FIELD

The embodiments discussed herein relate to a parallel computing apparatus, a compiling apparatus, and a parallel processing method.

BACKGROUND

There are cases in which a parallel computing device that is able to execute a plurality of threads in parallel by using a plurality of processors (processor cores, for example) is used. In an example of parallel processing executed by such a parallel computing device, different threads execute the same kind of operation on different input data in parallel, and each of the plurality of different threads generates intermediate data. Next, the intermediate data generated by the plurality of threads is aggregated to obtain resultant data. This parallel processing is sometimes called reduction processing. Among the compilers that generate object codes executed by parallel computing devices, some compilers generate, through optimization, an object code for reduction processing from a source code that has not been created for parallel processing.

In addition, there has been proposed a scheduling method for causing a plurality of processors to execute a plurality of threads in parallel with a shared memory. According to the proposed scheduling method, semaphores, message queues, message buffers, event flags, barriers, mutexes, etc. may be used as a synchronization mechanism for synchronizing the plurality of threads. These kinds of synchronization mechanism are used depending on the class of the threads to be synchronized.

In addition, there has been proposed a compiling device that generates an object code executable by a shared-memory parallel computing device. The proposed compiling device generates an object code that dynamically selects whether to parallelize processing within a loop by using a plurality of threads when the processing is executed. The generated object code calculates a threshold for the number of loops that could improve the execution efficiency on the basis of the number of instruction cycles per processing within a loop and predetermined parallelization overhead information. The object code executes the processing within a loop in parallel when the number of loops determined when the processing is executed is larger than the threshold. Otherwise, the object code sequentially executes the processing within a loop.

In addition, there has been proposed an operation processing apparatus that includes a plurality of cores that is able to execute threads in parallel and a shared memory. A single storage area in the shared memory is accessed exclusively. With the proposed operation processing apparatus, when two or more threads update data in the single storage area, these threads perform reduction processing before accessing the shared memory. In the reduction processing, the intermediate data generated by the threads is aggregated. In this way, the exclusive access to the single storage area in the shared memory is reduced.

See, for example, Japanese Laid-open Patent Publication Nos. 2005-43959, 2007-108838, and 2014-106715.

For example, each of a plurality of threads has previously been provided with a private area (for example, a stack area) on a memory, and the intermediate data generated by an individual thread is stored in the corresponding private area. In a first method for aggregating the intermediate data generated by a plurality of threads, an area for storing resultant data is allocated in a shared area on a memory, and each thread reflects its intermediate data in the resultant data in the shared area. However, according to this first method, since the resultant data is exclusively accessed by a plurality of threads, there is a problem that overhead is caused to perform the exclusive control.

In a second method for aggregating the intermediate data generated by a plurality of threads, each of the threads stores its intermediate data in a shared area, and one of the threads aggregates the intermediate data generated by the plurality of threads. However, according to the second method, an area for storing the intermediate data needs to be allocated in the shared area, in addition to the area for storing the resultant data. While each thread is able to use its private area without regard to the other threads, the plurality of threads share the shared area. Thus, allocation could be managed by control software such as the operating system (OS). Therefore, there is a problem that overhead is caused to allocate the area for storing the intermediate data. In particular, when the intermediate data is variable-length data such as a variable-length array, there is a problem that overhead is caused to dynamically allocate the area.

SUMMARY

According to one aspect, there is provided a parallel computing apparatus including: a first processor configured to execute a first thread; a second processor configured to execute a second thread; and a memory configured to include a first private area that corresponds to the first thread, a second private area that corresponds to the second thread, and a shared area, wherein the first processor stores first data in the first private area and stores address information that enables access to the first data in the shared area, and wherein the second processor stores second data in the second private area, accesses the first data based on the address information stored in the shared area, and generates third data based on the first data and the second data.

The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 illustrates a parallel computing device according to a first embodiment;

FIG. 2 illustrates a compiling device according to a second embodiment;

FIG. 3 illustrates an information processing system according to a third embodiment;

FIG. 4 is a block diagram illustrating a hardware example of a parallel computing device;

FIG. 5 is a block diagram illustrating a hardware example of a compiling device;

FIG. 6 illustrates an example of an array operation before parallelization;

FIG. 7 illustrates an example of a program before parallelization;

FIG. 8 illustrates an example of first reduction processing;

FIG. 9 illustrates an example of a first program after parallelization;

FIG. 10 illustrates an example of timing at which the first reduction processing is performed;

FIG. 11 illustrates an example of second reduction processing;

FIG. 12 illustrates an example of a second program after parallelization;

FIG. 13 illustrates an example of timing at which the second reduction processing is performed;

FIG. 14 illustrates examples of functions of the parallel computing device and the compiling device;

FIG. 15 is a flowchart illustrating an example of a procedure of reduction processing; and

FIG. 16 is a flowchart illustrating an example of a procedure of compilation.

DESCRIPTION OF EMBODIMENTS

Hereinafter, embodiments will be described with reference to the accompanying drawings, wherein like reference numerals refer to like elements throughout.

First Embodiment

First, a first embodiment will be described.

FIG. 1 illustrates a parallel computing device 10 according to a first embodiment.

The parallel computing device 10 according to the first embodiment is capable of executing a plurality of threads in parallel. For example, the parallel computing device 10 may be a client computer operated by a user or a server computer accessed by a client computer.

The parallel computing device 10 includes operation units 11 and 12 and a storage unit 13. For example, the operation units 11 and 12 are processors such as central processing units (CPUs) or CPU cores. For example, the operation units 11 and 12 execute programs stored in a memory such as the storage unit 13. The programs to be executed include a parallel processing program. The storage unit 13 is a volatile semiconductor memory such as a random access memory (RAM), for example.

In the first embodiment, the operation unit 11 executes a thread 14 a, and the operation unit 12 executes a thread 14 b. The storage unit 13 includes private areas 13 a and 13 b and a shared area 13 c. The private area 13 a is an area that corresponds to the thread 14 a and is a stack area allocated to the thread 14 a, for example. The private area 13 b is an area that corresponds to the thread 14 b and is a thread area allocated to the thread 14 b, for example. Both the threads 14 a and 14 b use the shared area 13 c.

The thread 14 a uses the private area 13 a on the basis of its address space. The thread 14 b uses the private area 13 b on the basis of an address space independent of the thread 14 a. The thread 14 a uses the private area 13 a without regard to the thread 14 b, and the thread 14 b uses the private area 13 b without regard to the thread 14 a. Thus, a relatively small cost is needed to dynamically allocate an area in the private area 13 a or 13 b. In contrast, since the shared area 13 c is used by both the threads 14 a and 14 b, the shared area 13 c is managed by control software such as an operating system (OS). Therefore, a relatively large cost is needed to dynamically allocate an area in the shared area 13 c.

The thread 14 a generates data 15 a (first data) as intermediate data and stores the data 15 a in the private area 13 a. The thread 14 b generates data 15 b (second data) as intermediate data and stores the data 15 b in the private area 13 b. The data 15 a and 15 b may be generated in parallel. The data 15 a and 15 b is aggregated, and data 15 d (third data) is generated as resultant data. Examples of the aggregation operation include: arithmetic operations such as addition, subtraction, and multiplication; logic operations such as a logical AND and a logical OR; and selection operations such as a maximal value selection and a minimum value selection. The data 15 d is stored in the shared area 13 c, for example.

The data 15 a stored in the private area 13 a is uniquely managed by the thread 14 a, and the data 15 a is not accessed by the thread 14 b in principle. In addition, the data 15 b stored in the private area 13 b is uniquely managed by the thread 14 b, and the data 15 b is not accessed by the thread 14 a in principle. In contrast, in the parallel computing device 10, the data 15 a in the private area 13 a and the data 15 b in the private area 13 b are efficiently aggregated as follows to generate the data 15 d.

The thread 14 a generates address information 15 c that enables access to the data 15 a in the private area 13 a and stores the address information 15 c in the shared area 13 c. For example, the address information 15 c is an initial physical address indicating the area in which the data 15 a is stored or an area in which a series of data including the data 15 a is stored. The thread 14 a may generate the address information 15 c after or before generating the data 15 a.

The thread 14 b reads the address information 15 c from the shared area 13 c and accesses the data 15 a in the private area 13 a on the basis of the address information 15 c. Next, the thread 14 b aggregates the data 15 a in the private area 13 a and the data 15 b in the private area 13 b, namely, the intermediate data generated by the threads 14 a and 14 b, and generates the data 15 d. The thread 14 b stores the generated data 15 d in the shared area 13 c, for example.

With the parallel computing device according to the first embodiment 10, the operation units 11 and 12 start the threads 14 a and 14 b, respectively. In addition, the thread 14 a stores the data 15 a in the private area 13 a and stores the address information 15 c in the shared area 13 c. The thread 14 b stores the data 15 b in the private area 13 b. In addition, the thread 14 b accesses the data 15 a on the basis of the address information 15 c and generates the data 15 d from the data 15 a and 15 b.

In this way, unlike the above second method in which the data 15 a and 15 b, which is the intermediate data, is stored in the shared area 13 c, since no area needs to be dynamically allocated in the shared area 13 c in the present embodiment, the overhead, which is caused by the above second method, is not caused in the present embodiment. In addition, unlike the above first method in which the thread 14 a reflects the data 15 a in the data 15 d and the thread 14 b reflects the data 15 b in the data 15 d, since exclusive control between the threads 14 a and 14 b is not performed in the present embodiment, the above overhead, which is caused by the first method in which exclusive control is performed, is not caused in the present embodiment. Thus, the data 15 a and 15 b generated by the threads 14 a and 14 b is aggregated at high speed. In addition, since the thread 14 b that has generated the data 15 b aggregates the data 15 a and 15 b, no new thread is started. Namely, while overhead is caused if a new thread is started, since no new thread is started in the present embodiment, no such overhead is caused in the present embodiment.

Second Embodiment

Next, a second embodiment will be described.

FIG. 2 illustrates a compiling device 20 according to a second embodiment.

The compiling device 20 according to the second embodiment generates a code executed by the parallel computing device 10 according to the first embodiment. The compiling device 20 may be a client computer operated by a user or a server computer accessed by a client computer. A single device may be configured to function as the parallel computing device 10 and the compiling device 20.

The compiling device 20 includes a storage unit 21 and a conversion unit 22. For example, the storage unit 21 is a volatile storage device such as a RAM or a non-volatile storage device such as a hard disk drive (HDD) or a flash memory. For example, the conversion unit 22 is a processor such as a CPU or a digital signal processor (DSP). The conversion unit 22 may include an electronic circuit for specific use, such as an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA). The processor executes programs stored in a memory, and the programs to be executed include a compiler program. A group of processors (multiprocessor) may be referred to as a “processor.”

The storage unit 21 holds a code 23 (a first code). The code 23 may be a source code, an intermediate code obtained by converting a source code, or an object code before optimization. The code 23 includes an instruction 23 a that indicates generating the data 15 d (first data). The conversion unit 22 converts the code 23 stored in the storage unit 21 into a code 24. The code 24 indicates starting the thread 14 a (a first thread) that generates the data 15 a (second data) and the thread 14 b (a second thread) that generates the data 15 b (third data) and the data 15 d on the basis of the data 15 a and 15 b. The code 24 may be a source code, an intermediate code, or an object code. For example, the code 24 is stored in the storage unit 21.

The code 24 obtained by converting the code 23 includes instructions 24 a to 24 d (first to fourth instructions).

The instruction 24 a indicates causing the thread 14 a to store the data 15 a in the private area 13 a that corresponds to the thread 14 a and causing the thread 14 b to store the data 15 b in the private area 13 b that corresponds to the thread 14 b. The storage of the data 15 a and the storage of the data 15 b may be executed in parallel. The instruction 24 b indicates causing the thread 14 a to store the address information 15 c that enables access to the data 15 a in the shared area 13 c. The instruction 24 c indicates causing the thread 14 b to access the data 15 a stored in the private area 13 a on the basis of the address information 15 c stored in the shared area 13 c. The instruction 24 d indicates causing the thread 14 b to aggregate the data 15 a and 15 b and generate the data 15 d.

With this compiling device according to the second embodiment 20, the parallel processing code 24 is generated from the code 23 that has not been created for parallel processing. In this way, the calculation is performed faster by utilizing operation capabilities of a computer. In addition, the intermediate data generated by the threads is aggregated faster. Namely, unlike the above second method in which the data 15 a and 15 b is stored in the shared area 13 c, since no area needs to be dynamically allocated in the shared area 13 c in the present embodiment, the overhead, which is caused by the above second method, is not caused in the present embodiment. In addition, unlike the above first method in which the thread 14 a reflects the data 15 a in the data 15 d and the thread 14 b reflects the data 15 b in the data 15 d, since exclusive control between the threads 14 a and 14 b is not performed in the present embodiment, the above overhead, which is caused by the first method in which exclusive control is performed, is not caused in the present embodiment. Thus, since the thread 14 b that has generated the data 15 b aggregates the data 15 a and 15 b, no new thread is started. Namely, while overhead is caused if a new thread is started, since no new thread is started in the present embodiment, no such overhead is caused in the present embodiment.

Third Embodiment

Next, a third embodiment will be described.

FIG. 3 illustrates an information processing system according to a third embodiment.

The information processing system according to the third embodiment includes a parallel computing device 100 and a compiling device 200. The parallel computing device 100 and the compiling device 200 are connected to each other via a network 30. Each of the parallel computing device 100 and the compiling device 200 may be a client computer operated by a user or a server computer accessed by a client computer via the network 30. The parallel computing device 100 corresponds to the parallel computing device 10 according to the first embodiment. The compiling device 200 corresponds to the compiling device 20 according to the second embodiment.

The parallel computing device 100 is a shared-memory multiprocessor that executes a plurality of threads in parallel by using a plurality of CPU cores. The compiling device 200 converts a source code created by a user into an object code executable by the parallel computing device 100. The compiling device 200 is able to generate a parallel processing object code that enables starting a plurality of threads that operate in parallel from a source code that has not been created for parallel processing. The compiling device 200 transmits the generated object code to the parallel computing device 100. While the device that compiles a program and the device that executes the program are separately arranged in the third embodiment, a single device may be configured to compile and execute the program.

FIG. 4 is a block diagram illustrating a hardware example of the parallel computing device 100.

The parallel computing device 100 includes a CPU 101, a RAM 102, an HDD 103, an image signal processing unit 104, an input signal processing unit 105, a media reader 106, and a communication interface 107. These units are connected to a bus 108.

The CPU 101 is a processor that executes program instructions. The CPU 101 loads at least part of a program or data stored in the HDD 103 to the RAM 102 and executes a program. The CPU 101 includes CPU cores 101 a to 101 d. The CPU cores 101 a to 101 d are able to execute threads in parallel. In addition, each of the CPU cores 101 a to 101 d includes a cache memory faster than the RAM 102. The number of CPU cores included in the CPU 101 is not limited. Namely, the CPU 101 may include two or more CPU cores. Each of or the group of the CPU cores 101 a to 101 d may be referred to as a “processor.” In addition, the CPU 101 may be referred to as a “processor.”

The RAM 102 is a volatile semiconductor memory that temporarily holds programs executed by the CPU 101 or data used by the CPU 101 for operations. The parallel computing device 100 may include a different kind of memory other than the RAM. The parallel computing device 100 may include a plurality of memories.

The HDD 103 is a non-volatile storage device that holds an OS, middleware, software programs such as application software, and data. The programs include a program compiled by the compiling device 200. The parallel computing device 100 may include a different kind of storage device such as a flash memory or a solid state drive (SSD). The parallel computing device 100 may include a plurality of non-volatile storage devices.

The image signal processing unit 104 outputs an image to a display 111 connected to the parallel computing device 100 in accordance with an instruction from the CPU 101. Examples of the display 111 include a cathode ray tube (CRT) display, a liquid crystal display (LCD), a plasma display panel (PDP), and an organic electro-luminescence (OEL) display.

The input signal processing unit 105 acquires an input signal from an input device 112 connected to the parallel computing device 100 and outputs the input signal to the CPU 101. Examples of the input device 112 include a pointing device such as a mouse, a touch panel, a touch pad, or a trackball, a keyboard, a remote controller, and a button switch. A plurality of kinds of input device may be connected to the parallel computing device 100,

The media reader 106 is a reading device that reads programs or data recorded in a recording medium 113. Examples of the recording medium 113 include a magnetic disk such as a flexible disk (FD) or an HDD, an optical disc such as a compact disc (CD) or a digital versatile disc (DVD), a magneto-optical disk (MO), and a semiconductor memory. For example, the media reader 106 stores a program or data read from the recording medium 113 in the RAM 102 or the HDD 103.

The communication interface 107 is an interface that is connected to the network 30 and that communicates with other devices such as the compiling device 200 via the network 30. The communication interface 107 may be a wired communication interface connected to a communication device such as a switch via a cable or a wireless communication interface connected to a base station via a wireless link.

The media reader 106 may be absent in the parallel computing device 100. The image signal processing unit 104 and the input signal processing unit 105 may be absent in the parallel computing device 100 if a terminal operated by a user has the equivalent functions. The display 111 or the input device 112 may be incorporated in the enclosure of the parallel computing device 100. The CPU cores 101 a and 101 b correspond to the operation units 11 and 12 according to the first embodiment, respectively. The RAM 102 corresponds to the storage unit 13 according to the first embodiment.

FIG. 5 is a block diagram illustrating a hardware example of the compiling device 200.

The compiling device 200 includes a CPU 201, a RAM 202, an HDD 203, an image signal processing unit 204, an input signal processing unit 205, a media reader 206, and a communication interface 207. These units are connected to a bus 208.

The CPU 201 has functions equivalent to those of the CPU 101 in the parallel computing device 100. However, the CPU 201 may include only one CPU core and does not need to be a multiprocessor. The RAM 202 has functions equivalent to those of the RAM 102 in the parallel computing device 100. The HDD 203 has functions equivalent to those of the HDD 103 in the parallel computing device 100. The programs stored in the HDD 203 include a compiler program.

The image signal processing unit 204 has functions equivalent to those of the image signal processing unit 104 in the parallel computing device 100. The image signal processing unit 204 outputs an image to a display 211 connected to the compiling device 200. The input signal processing unit 205 has functions equivalent to those of the input signal processing unit 105 in the parallel computing device 100. The input signal processing unit 205 acquires an input signal from an input device 212 connected to the compiling device 200.

The media reader 206 has functions equivalent to those of the media reader 106 in the parallel computing device 100. The media reader 206 reads programs or data recorded in a recording medium 213. The recording medium 113 and the recording medium 213 may be the same medium. The communication interface 207 has functions equivalent to those of the communication interface 107 in the parallel computing device 100. The communication interface 207 is connected to the network 30.

The media reader 206 may be absent in the compiling device 200. The image signal processing unit 204 and the input signal processing unit 205 may be absent in the compiling device 200 if a terminal operated by a user has the equivalent functions. The display 211 or the input device 212 may be incorporated in the enclosure of the compiling device 200. The CPU 201 corresponds to the conversion unit 22 according to the second embodiment. The RAM 202 corresponds to the storage unit 21 according to the second embodiment.

Next, an array operation executed by the parallel computing device 100 will be described.

FIG. 6 illustrates an example of an array operation before parallelization.

In this operation, a two-dimensional (2D) array 41 (a 2D array a) of n rows and m columns (each of “n” and “m” is an integer of 2 or more) is given as input data. In addition, an array 42 (an array sum) of n rows is generated from the 2D array 41 as resultant data.

The parallel computing device 100 aggregates the values of all the columns in an i-th row (i=1 to n) in the 2D array 41 and stores the sum in the i-th row in the array 42. Namely, the parallel computing device 100 stores the sum of a(1,1) to a(1,m) in sum(1). In addition, the parallel computing device 100 stores the sum of a(2,1) to a(2,m) in sum(2). In addition, the parallel computing device 100 stores the sum of a(n,1) to a(n,m) in sum(n). For each of description, the following description will be made by using relatively small input data of 4 rows and 8 columns as an example, as needed.

The parallel computing device 100 is able to parallelize the array operation by using the CPU cores 101 a to 101 d (reduction processing). The parallel computing device 100 divides the 2D array 41 into a plurality of column groups and allocates a divided column group to an individual one of the CPU cores 101 a to 101 d. For example, the 1st and 2nd columns are allocated to the CPU core 101 a, the 3rd and 4th columns to the CPU core 101 b, the 5th and 6th columns to the CPU core 101 c, and the 7th and 8th columns to the CPU core 101 d. Each of the CPU cores 101 a to 101 d aggregates the values in its allocated column group in the 2D array 41 per row and generates intermediate data. The array 42 is generated by aggregating the intermediate data generated by the CPU cores 101 a to 101 d per row.

FIG. 7 illustrates an example of a program before parallelization.

A source code 51 represents the array operation illustrated in FIG. 6. The compiling device 200 compiles the source code 51 to generate an object code executed by the parallel computing device 100. In the source code 51, the integers n and m, the array sum of n rows of an integer type, and the 2D array a of n rows and m columns of an integer type are defined. In the source code 51, loop variables i and j are also defined. In addition, in the source code 51, a nested loop including an outer loop in which the value of the loop variable j is increased from 1 to m by 1 and an inner loop in which the value of the loop variable i is increased from 1 to n by 1 is defined. In the inner loop, an operation of adding a(i,j) to sum(i) is defined. Namely, the source code 51 indicates performing sequential processing on the 2D array 41 from the first to m-th column.

In the source code 51, an Open Multi-Processing (MP) directive is added in the nested loop section. The OpenMP directive is a parallelization directive added by the user to the source code 51. When a compile option for enabling the OpenMP directive is specified, the compiling device 200 generates a parallel processing object code from the source code 51 within the range to which the OpenMP directive is added. In contrast, a compile option for enabling the OpenMP directive is not specified, the compiling device 200 ignores the OpenMP directive and generates a sequential processing object code from the source code 51.

More specifically, in the source code 51, a reduction directive specifying “+” as a reduction operator and “sum” as a reduction variable is added. The reduction operator “+” indicates aggregating the intermediate data generated by a plurality of threads in parallel through addition. Other reduction operators such “−” (subtraction), “×” (multiplication), “.AND.” (logical AND), “.OR.” (logical OR), “MAX” (maximal value selection), and “MIN” (minimum value selection) and other user-defined operators may be used. The reduction variable “sum” indicates that the variable for storing the final resultant data is the array sum.

Next, two methods for realizing the reduction processing will be described.

FIG. 8 illustrates an example of first reduction processing.

The following description will be made assuming that the parallel computing device 100 uses the CPU cores 101 a to 101 d to execute four threads in parallel. The CPU cores 101 a to 101 d start threads #0 to #3, respectively.

The parallel computing device 100 allocates a stack area 121 a that corresponds to the thread #0 in the RAM 102. The stack area 121 a is a storage area that locally stores data generated by the thread #0. The thread #0 is able to use the stack area 121 a independently of the other threads on the basis of its address space. Even when variable-length data is stored, a memory area is not dynamically allocated to the stack area 121 a by the OS. Thus, the cost of the usage is relatively small. Likewise, the parallel computing device 100 allocates stack areas 121 b to 121 d that correspond to the threads #1 to #3, respectively, in the RAM 102.

In addition, the parallel computing device 100 allocates a shared area 122 in the RAM 102. The shared area 122 is a storage area accessible by the threads #0 to #3. When variable-length data is stored, a memory area is dynamically allocated to the shared area 122 by the OS. Thus, the cost of the usage is larger than that of the stack areas 121 a to 121 d. In addition, when two or more threads simultaneously access a single area in the shared area 122, exclusive control is performed.

When parallelizing the array operation illustrated in FIGS. 6 and 7, the thread #0 generates an array 43 a (array sum0), which is a copy of the reduction variable “sum,” in the stack area 121 a. Likewise, the threads #1 to #3 generate arrays 43 b to 43 d (arrays sum1 to sum3), which are copies of the reduction variable “sum,” in the stack areas 121 b to 121 d, respectively. In addition, the parallel computing device 100 generates the array 42 (array sum), which is the original of the reduction variable “sum,” in the shared area 122. Attributes of the arrays 43 a to 43 d such as the data type, dimension, and length are the same as those of the array 42.

The 1st and 2nd columns in the 2D array 41 are allocated to the thread #0. The thread #0 performs an array operation on the 1st and 2nd columns, the array operation being a subset of the array operation performed on the entire 2D array 41, and stores the obtained intermediate data in the array 43 a. Namely, the thread #0 stores the sum of a(i,1) and a(i,2) in sum0(i) (i=1 to 4).

Likewise, the 3rd and 4th columns in the 2D array 41 are allocated to the thread #1. The thread #1 stores the sum of a(i,3) and a(i,4) in sum1(i) (i=1 to 4). The 5th and 6th columns in the 2D array 41 are allocated to the thread #2. The thread #2 stores the sum of a(i,5) and a(i,6) in sum2(i) (i=1 to 4). The 7th and 8th columns in the 2D array 41 are allocated to the thread #3. The thread #3 stores the sum of a(i,7) and a(i,8) in sum3(i) (i=1 to 4).

The intermediate data to be stored in the arrays 43 a to 43 d may be generated by the threads #0 to #3 in parallel. The parallel computing device 100 aggregates the intermediate data stored in the arrays 43 a to 43 d and stores the resultant data in the array sum. According to the first method, the parallel computing device 100 aggregates the intermediate data as follows.

The thread #0 adds a value stored in the array 43 a in the stack area 121 a to the corresponding value in the array 42 in the shared area 122. Namely, the thread #0 adds sum0(i) to sum(i) (i=1 to 4). The thread #1 adds a value stored in the array 43 b in the stack area 121 b to the corresponding value in the array 42 in the shared area 122. Namely, the thread #1 adds sum1(i) to sum(i) (i=1 to 4). The thread #2 adds a value stored in the array 43 c in the stack area 121 c to the corresponding value in the array 42 in the shared area 122. Namely, the thread #2 adds sum2(i) to sum(i) (i=1 to 4). The thread #3 adds a value stored in the array 43 d in the stack area 121 d to the corresponding value in the array 42 in the shared area 122. Namely, the thread #3 adds sum3(i) to sum(i) (i=1 to 4).

In this way, sum(i) represents the sum of sum0(i) to sum3(i). Namely, sum(i) cacluated in this way signifies the sum of a(i,1) to a(i,8). Thus, whether parallelization is performed or not, the same resultant data is stored in the array 42 in principle. However, depending on the variable type, for example, when an element in the array 42 is a floating-point number, the order of operations could be changed, and as a result, an operation error could occur. In addition, according to the first method, each of the threads #0 to #3 accesses all the rows in the array 42. Thus, since the threads #0 to #3 exclusively access the array 42, parallelization is not substantially performed.

FIG. 9 illustrates an example of a first program after parallelization.

For each of description, the parallel processing code generated from the source code 51 illustrated in FIG. 7 is represented in source code format. In reality, a processing code based on the OpenMP reduction directive is generated by using an intermediate code.

The source code 52 is a parallel processing code obtained by converting the source code 51 in accordance with the first method illustrated in FIG. 8. As in the source code 51, the integers n and m, the array sum of n rows of an integer type, the 2D array a of n rows and m columns of an integer type, and the loop variables i and j are defined in the source code 52. In addition, an array sum_k of n rows of an integer type is defined in the source code 52, as a copy of the array sum, which is the reduction variable. The array sum_k corresponds to the arrays sum0 to sum3 in FIG. 8. The array sum, which is the original variable, is assumed to have been defined as a shared variable in an upper module. However, since the array sum_k, which is a copied variable, appears only in this subroutine, the array sum_k is determined to be a private variable when compilation is performed.

In addition, a code for initializing the array sum_k is inserted in the source code 52. The initial value of the array sum_k is determined based on the reduction operator. For example, when the reduction operator is “+” or “−,” the initial value in each row in the array sum_k is 0. When the reduction operators are “×,” “.AND.,” and “.OR.,” the initial values are “1,” “TRUE.,” and “FALSE.,” respectively. When the reduction operators are “MAX” and “MIN,” the initial values are the minimum possible value and the maximum possible value, respectively.

In addition, as in the source code 51, a nested loop including an outer loop in which the value of the loop variable j is increased from 1 to m by 1 and an inner loop in which the value of the loop variable i is increased from 1 to n by 1 is defined in the source code 52. In the inner loop, an operation of adding a(i,j) to sum_k(i) used in place of sum(i) is defined. This indicates that each of the plurality of threads stores intermediate data in a private variable, namely, not in the original shared variable but in a copy thereof. In the source code 52 illustrated in FIG. 9, description of the division of the array a into column groups is omitted.

In addition, a code for aggregating the intermediate data stored in the array sum_k, which is a private variable, in the array sum, which is the shared variable, is inserted into the source code 52. More specifically, a code for adding sum_k(i) to sum(i) (i=1 to n) is inserted into the source code 52. In the source code 52 illustrated in FIG. 9, description of exclusive control performed when the array sum is accessed is omitted.

FIG. 10 illustrates an example of timing at which the first reduction processing is performed.

In the first method, when the threads #0 to #3 aggregate their intermediate data, parallelization is not substantially performed. For example, first, the thread #0 locks the array 42 and prevents the other threads from accessing the array 42. The thread #0 adds sum0(1) to sum(1), sum0(2) to sum(2), sum0(3) to sum(3), and sum0(4) to sum(4). Next, the thread #0 unlocks the array 42 (P10), and one of the other threads is allowed to access the array 42.

Next, the thread #2 locks the array 42 and prevents the other threads from accessing the array 42. The thread #2 adds sum2(1) to sum(1), sum2(2) to sum(2), sum2 (3) to sum(3), and sum2 (4) to sum(4). Next, the thread #2 unlocks the array 42 (P12), and one of the other threads is allowed to access the array 42.

Next, the thread #1 locks the array 42 and prevents the other threads from accessing the array 42. The thread #1 adds sum1(1) to sum(1), sum1(2) to sum(2), sum1 (3) to sum(3), and sum1 (4) to sum(4). Next, the thread #1 unlocks the array 42 (P11), and one of the other threads is allowed to access the array 42.

Finally, the thread #3 locks the array 42. The thread #3 adds sum3(1) to sum(1), sum3(2) to sum(2), sum3 (3) to sum(3), and sum3 (4) to sum(4). Next, the thread #3 unlocks the array 42 (P13). The above order in which the threads #0 to #3 lock the array 42 is only an example. The threads #0 to #3 may lock the array 42 in a different order, depending on their execution statuses.

With this method in which the threads #0 to #3 lock the array 42 when aggregating their intermediate data, the threads #0 to #3 sequentially access the array 42. Namely, one of the threads #0 to #3 that locks the array first reflects its intermediate data in the array 42, and the other threads need to wait until the array 42 is unlocked. Thus, since the aggregation of the intermediate data is not parallelized, there is a problem that a certain length of time is needed. There is another method in which the arrays 43 a to 43 d are stored in the shared area 122 instead of in the stack areas 121 a to 121 d. In this way, the threads #0 to #3 are able to access all the intermediate data and aggregate their intermediate data without locking the array 42. However, according to this method, when the arrays 43 a to 43 d are variable-length data, there is a problem that overhead is caused to dynamically allocate an area in the shared area 122. To solve this problem, the parallel computing device 100 may perform reduction processing according to a second method described below.

FIG. 11 illustrates an example of second reduction processing.

As in the first method, the thread #0 generates the array 43 a (array sum0) in the stack area 121 a. The thread #1 generates the array 43 b (array sum1) in the stack area 121 b. The thread #2 generates the array 43 c (array sum2) in the stack area 121 c. The thread #3 generates the array 43 d (array sum3) in the stack area 121 d. The parallel computing device 100 generates the array 42 (array sum) in the shared area 122.

In addition, the parallel computing device 100 generates a pointer array 44 (a pointer array adr) in the shared area 122. The pointer array 44 holds addresses that indicate the locations of the arrays 43 a to 43 d on the RAM 102 (for example, physical addresses that indicate the heads of the arrays 43 a to 43 d, respectively). The thread #0 stores the address of the array 43 a in a row that corresponds to the thread #0 in the pointer array 44. The thread #1 stores the address of the array 43 b in a row that corresponds to the thread #1 in the pointer array 44. The thread #2 stores the address of the array 43 c in a row that corresponds to the thread #2 in the pointer array 44. The thread #3 stores the address of the array 43 d in a row that corresponds to the thread #3 in the pointer array 44.

The threads #0 to #3 generate their intermediate data in the same way as in the above first method. The second method differs from the first method in aggregating the intermediate data. The parallel computing device 100 divides the array 42 into rows and allocates a row to each of the threads #0 to #3. Of all the intermediate data stored in the arrays 43 a to 43 d, each of the threads #0 to #3 aggregates the intermediate data corresponding to the row allocated thereto and stores the resultant data in the array 42. Since each of the threads #0 to #3 accesses a different row of all the rows in the array 42, the intermediate data is aggregated in parallel. Each of the threads #0 to #3 is able to access the stack areas that correspond to the other threads on the basis of the addresses stored in the pointer array 44.

For example, the threads #0 to #3 handle the 1st to 4th columns, respectively. The thread #0 reads sum0(1) from the stack area 121 a. In addition, the thread #0 refers to the pointer array 44 and reads sum1(1) from the stack area 121 b, sum2(1) from the stack area 121 c, and sum3(1) from the stack area 121 d. The thread #0 stores the sum of sum0(1) to sum3(1) in sum(1) in the shared area 122.

Likewise, the thread #1 refers to the pointer array 44 and reads sum0(2) from the stack area 121 a, sum1(2) from the stack area 121 b, sum2(2) from the stack area 121 c, and sum3(2) from the stack area 121 d. The thread #1 stores the sum of the sum0(2) to sum3(2) in sum(2) in the shared area 122.

The thread #2 refers to the pointer array 44 and reads sum0(3) from the stack area 121 a, sum1(3) from the stack area 121 b, sum2(3) from the stack area 121 c, and sum3(3) from the stack area 121 d. The thread #2 stores the sum of sum0(3) to sum3(3) in sum(3) in the shared area 122.

The thread #3 refers to the pointer array 44 and reads sum0(4) from the stack area 121 a, sum1(4) from the stack area 121 b, sum2(4) from the stack area 121 c, and sum3(4) from the stack area 121 d. The thread #3 stores the sum of sum0(4) to sum3(4) in sum(4) in the shared area 122.

In this way, sum(1) represents the sum of a(1,1) to a(1,8), and sum(2) represents the sum of a(2,1) to a(2,8). In addition, sum(3) represents the sum of a(3,1) to a(3,8), and sum(4) represents the sum of a(4,1) to a(4,8). Thus, the resultant data stored in the array 42 according to the second method matches the resultant data obtained when parallelization is not performed or the resultant data obtained according to the first method in principle. However, depending on the variable type, for example, when an element in the array 42 is a floating-point number, the order of operations could be changed, and as a result, an operation error could occur. In addition, according to the second method, since each of the threads #0 to #3 accesses a different row in the array 42, the intermediate data is aggregated in parallel without exclusive control.

Each of the CPU cores 101 a to 101 d includes a cache memory. When accessing data, each of the CPU cores 101 a to 101 d loads the data from the RAM 102 to its cache memory. Each of the CPU cores 101 a to 101 d loads data to its cache memory on the basis of a certain size called a cache line. When a first CPU core and a second CPU core access different data, if the locations of both of the data on the RAM 102 are closer to each other than the cache line size, the data is read to both of the cache memories of the first and second CPU cores.

If this happens, a problem with data consistency between the cache memories arises. When the first CPU core updates data on its cache memory, the second CPU core performs reading from the RAM 102 after discarding the entire cache line including the data. This problem is often referred to as “false sharing between cache memories.” False sharing could deteriorate the data access performance.

Thus, to avoid false sharing, when the threads #0 to #3 of the parallel computing device 100 store their addresses in the pointer array 44, the threads #0 to #3 separate the rows in which the addresses are stored from each other. Namely, when one thread and another thread store their respective addresses, these addresses are separated from each other more than the cache line size. For example, when the cache line size is 128 bytes and the size of a single address is 8 bytes, the address stored by one thread and the address stored by another thread are separated by 16 rows or more.

In this case, the pointer array 44 has a length corresponding to the number of threads×16. The thread #0 stores an address in the 1st row in the pointer array 44. The thread #1 stores an address in the 17th row in the pointer array 44. The thread #2 stores an address in the 33rd row in the pointer array 44. The thread #3 stores an address in the 49th row in the pointer array 44. No rows other than the above rows are used. In this way, since the addresses of different threads are not read to the same cache line, false sharing is avoided.

If the number of threads that are started is dynamically determined at the time of an execution, the pointer array 44 having a length based on the maximum thread number may statically be generated in the shared area 122. The number of CPU cores may be estimated as the maximum thread number. For example, when the CPU 101 includes four CPU cores (CPU cores 101 a to 101 d), the maximum thread number is estimated as 4. In this way, since an area is statically allocated to the pointer array 44 when compilation is performed, overhead to dynamically allocate an area in the shared area 122 is not caused.

False sharing between cache memories could occur when the threads #0 to #3 access the array 42. Thus, it is preferable that a row handled by one thread and a row handled by another thread in the array 42 be seprated by the cache line size or more. For example, when the cache line size is 128 bytes and the size of a single integer is 8 bytes, it is preferable that each thread handle at least 16 rows in the array 42.

To avoid false sharing, the parallel computing device 100 may select an intermediate data aggregation method on the basis of the number of rows in the array 42. For example, when the length of the array 42, which is the reduction variable, corresponds to the number of threads×15 rows or less, the parallel computing device 100 aggregates the intermediate data according to the first method illustrated in FIG. 8. In contrast, when the length of the array 42 corresponds to the number of threads×16 rows or more, the parallel computing device 100 aggregates the intermediate data according to the second method.

FIG. 12 illustrates an example of a second program after parallelization.

For ease of description, the parallel processing code generated from the source code 51 illustrated in FIG. 7 is represented in source code format. A source code 53 is a parallel processing code obtained by converting the source code 51 in accordance with the second method illustrated in FIG. 11.

As in the source codes 51 and 52, the integers n and m, the array sum of n rows of an integer type, the 2D array a of n rows and m columns of an integer type, and the loop variables i and j are defined in the source code 53. In addition, as in the source code 52, an array sum_k of n rows of an integer type is defined in the source code 53, as a copy of the array sum, which is the reduction variable.

In addition, the pointer array adr of tn×16 rows of an integer type is defined in the source code 53 (tn represents the number of threads determined based on the target CPU). The pointer array adr is handled as a shared variable by adding a save attribute. In addition, an array var of n rows of an integer type is defined in the source code 53. In addition, a pointer ptr is defined in the source code 53. The pointer ptr is an address that indicates the head of data, and the data indicated by the pointer ptr is accessed as the array var.

In addition, a code for storing the address of the array sum_k in the (tid×16+1)th row in the pointer array adr is inserted in the source code 53 (tid represents a thread ID). In this way, the addresses of the threads #0 to #3 are stored while being separated from each other by 16 rows. In addition, as in the source code 52, a code for initializing the array sum_k is inserted in the source code 53. In addition, as in the source code 52, a nested loop including an outer loop in which the value of the loop variable j is increased from 1 to m by 1 and an inner loop in which the value of the loop variable i is increased from 1 to n by 1 is defined in the source code 53. In the inner loop, an operation of adding a(i,j) to sum_k(i) used in place of sum(i) is defined. In the source code 53 illustrated in FIG. 12, description of the division of the array a into column groups is omitted.

In addition, a code for aggregating the intermediate data stored in the array sum_k, which is a private variable, in the array sum, which is a shared variable, is inserted into the source code 53. More specifically, a nested loop including an outer loop in which the value of the loop variable j is increased from 0 to tn−1 by 1 and an inner loop in which the value of the loop variable i is increased from 1 to n by 1 is defined in the source code 53. Between the outer and inner loops, a code for referring to the address in the (j×16+1)th row in the pointer array adr as the pointer ptr is inserted. In the inner loop, a code for adding the i-th row in the array var indicated by the pointer ptr to sum(i) is inserted. In FIG. 12, description of the division of the array sum into rows is omitted.

In addition, in the source code 53, before and after the code for aggregating the intermediate data, directives indicating barrier synchronization are inserted. Barrier synchronization is synchronization processing in which processing performed by a plurality of threads is controlled until the processing reaches a predetermined point. Since barrier synchronization is performed immediately before the aggregation of the intermediate data is started, the threads #0 to #3 do not start their aggregation until all the threads #0 to #3 finish generating the intermediate data. This is because each thread accesses the intermediate data generated by the other threads. In addition, since barrier synchronization is performed immediately after the aggregation of the intermediate data is ended, the threads #0 to #3 do not start the next processing until all the threads #0 to #3 finish aggregating the intermediate data. This is to prevent the intermediate data from being deleted from the stack areas 121 a to 121 d before the completion of the aggregation.

There are some methods for realizing the above barrier synchronization. For example, when the CPU cores 101 a to 101 d support barrier synchronization, a register included in each of the CPU cores 101 a to 101 d is provided with flags corresponding to all the CPU cores. If a CPU core has its processing proceed to a predetermined point, the CPU core halts the processing, notifies the other CPU cores of the status, and changes the flag corresponding to the CPU core from 0 to 1. When all the flags corresponding to the CPU cores 101 a to 101 d represent 1, the CPU cores resume their processing. The shared area 122 may be provided with flags corresponding to the CPU cores 101 a to 101 d.

FIG. 13 illustrates an example of timing at which the second reduction processing is performed.

In the second method, the threads #0 to #3 are able to aggregate their intermediate data in parallel. First, in accordance with barrier synchronization, the threads #0 to #3 wait until the threads #0 to #3 finish generating their intermediate data. When the threads #0 to #3 finish generating their intermediate data, the thread #0 refers to the pointer array 44, accesses sum0(1), and adds sum0(1) to sum(1). The thread #0 refers to the pointer array 44, accesses sum1(1), and adds sum1(1) to sum(1). The thread #0 refers to the pointer array 44, accesses sum2(1), and adds sum2(1) to sum(1). The thread #0 refers to the pointer array 44, accesses sum3(1), and adds sum3(1) to sum(1) (P20).

In addition, when the threads #0 to #3 finish generating their intermediate data, in parallel with the thread #0, the thread #1 refers to the pointer array 44, accesses sum0(2), and adds sum0(2) to sum(2). The thread #1 refers to the pointer array 44, accesses sum1(2), and adds sum1(2) to sum(2). The thread #1 refers to the pointer array 44, accesses sum2(2), and adds sum2(2) to sum(2). The thread #1 refers to the pointer array 44, accesses sum3(2), and adds sum3(2) to sum(2) (P21).

In addition, when the threads #0 to #3 finish generating their intermediate data, in parallel with the threads #0 and #1, the thread #2 refers to the pointer array 44, accesses sum0(3), and adds sum0(3) to sum(3). The thread #2 refers to the pointer array 44, accesses sum1(3), and adds sum1(3) to sum(3). The thread #2 refers to the pointer array 44, accesses sum2(3), and adds sum2(3) to sum(3). The thread #2 refers to the pointer array 44, accesses sum3(3), and adds sum3(3) to sum(3) (P22).

In addition, when the threads #0 to #3 finish generating their intermediate data, in parallel with the threads #0 to #2, the thread #3 refers to the pointer array 44, accesses sum0(4), and adds sum0(4) to sum(4). The thread #3 refers to the pointer array 44, accesses sum1(4), and adds sum1(4) to sum(4). The thread #3 refers to the pointer array 44, accesses sum2(4), and adds sum2(4) to sum(4). The thread #3 refers to the pointer array 44, accesses sum3(4), and adds sum3(4) to sum(4) (P23).

Next, in accordance with barrier synchronization, the threads #0 to #3 wait until the threads #0 to #3 finish aggregating their intermediate data. When the threads #0 to #3 finish aggregating their intermediate data, the thread #0 may delete the array 43 a from the stack area 121 a. The thread #1 may delete the array 43 b from the stack area 121 b. The thread #2 may delete the array 43 c from the stack area 121 c. The thread #3 may delete the array 43 d from the stack area 121 d.

Next, functions of the parallel computing device 100 and the compiling device 200 will be described.

FIG. 14 illustrates examples of functions of the parallel computing device 100 and the compiling device 200.

The parallel computing device 100 includes the stack areas 121 a to 121 d, the shared area 122, and threads 123 a to 123 d. The stack areas 121 a to 121 d and the shared area 122 may be realized as storage areas allocated on the RAM 102. The thread 123 a to 123 d may be realized as program modules executed by the CPU 101. The program modules that realize the thread 123 a to 123 d are generated by the compiling device 200. The threads 123 a to 123 d are executed by the CPU cores 101 a to 101 d, respectively

The stack areas 121 a to 121 d hold the arrays 43 a to 43 d, respectively, and the shared area 122 holds the array 42 and the pointer array 44.

The thread 123 a generates the array 43 a in the stack area 121 a and stores the address of the array 43 a in the pointer array 44. In addition, the thread 123 a performs an array operation on the columns allocated thereto among the column groups in the 2D array 41 and stores the intermediate data in the array 43 a. In addition, the thread 123 a accesses the arrays 43 a to 43 d by referring to the pointer array 44, performs a reduction operation on a row allocated thereto among the rows in the arrays 43 a to 43 d, and stores the resultant data in the array 42.

Likewise, the thread 123 b generates the array 43 b in the stack area 121 b and stores the address of the array 43 b in the pointer array 44. In addition, the thread 123 b performs an array operation on the columns allocated thereto among the column groups in the 2D array 41 and stores the intermediate data in the array 43 b. In addition, the thread 123 b accesses the arrays 43 a to 43 d by referring to the pointer array 44, performs a reduction operation on a row allocated thereto among the rows in the arrays 43 a to 43 d, and stores the resultant data in the array 42.

Likewise, the thread 123 c generates the array 43 c in the stack area 121 c and stores the address of the array 43 c in the pointer array 44. In addition, the thread 123 c performs an array operation on the columns allocated thereto among the column groups in the 2D array 41 and stores the intermediate data in the array 43 c. In addition, the thread 123 c accesses the arrays 43 a to 43 d by referring to the pointer array 44, performs a reduction operation on a row allocated thereto among the rows in the arrays 43 a to 43 d, and stores the resultant data in the array 42.

Likewise, the thread 123 d generates the array 43 d in the stack area 121 d and stores the address of the array 43 d in the pointer array 44. In addition, the thread 123 d performs an array operation on the columns allocated thereto among the column groups in the 2D array 41 and stores the intermediate data in the array 43 d. In addition, the thread 123 d accesses the arrays 43 a to 43 d by referring to the pointer array 44, performs a reduction operation on a row allocated thereto among the rows in the arrays 43 a to 43 d, and stores the resultant data in the array 42.

The threads 123 a to 123 d correspond to the threads #0 to #3 in FIG. 13, respectively.

The compiling device 200 includes a source code storage unit 221, an intermediate code storage unit 222, an object code storage unit 223, a front-end unit 224, an optimization unit 225, and a back-end unit 226. The source code storage unit 221, the intermediate code storage unit 222, and the object code storage unit 223 may be realized as storage areas allocated in the RAM 202 or the HDD 203. The front-end unit 224, the optimization unit 225, and the back-end unit 226 may be realized as program modules executed by the CPU 201.

The source code storage unit 221 holds a source code (for example, the source code 51 in FIG. 7) created by a user. The source code is written in a high level language such as Fortran. A source code that is not created for parallel processing may be used. An OpenMP directive that instructs parallelization may be included in the source code. The intermediate code storage unit 222 holds an intermediate code converted from the source code. The intermediate code is written in an intermediate language used in the compiling device 200. The object code storage unit 223 holds a machine-readable object code that corresponds to the source code. The object code is executed by the parallel computing device 100.

The front-end unit 224 performs front-end processing of compilation. Namely, the front-end unit 224 reads the source code from the source code storage unit 221 and analyzes the read source code. The analysis of the source code includes lexical analysis, syntax analysis, and semantic analysis. The front-end unit 224 generates an intermediate code that corresponds to source code and stores the generated intermediate code in the intermediate code storage unit 222.

The optimization unit 225 reads the intermediate code from the intermediate code storage unit 222 and performs various kinds of optimization on the intermediate code so that an object code having a high execution efficiency is generated. The optimization includes parallelization in which a plurality of CPU cores are used. If the optimization unit 225 has an automatic parallelization function, the optimization unit 225 detects processing that can be performed in parallel from the intermediate code and rewrites the intermediate code so that a plurality of threads are executed in parallel. In addition, if an OpenMP directive is added in the source code and a compile option for enabling the OpenMP directive is specified, the optimization unit 225 rewrites the intermediate code so that the processing to which the OpenMP directives is added is performed in parallel. In particular, if a reduction directive is added in the source code, the optimization unit 225 rewrites the intermediate code so that a plurality of threads perform the reduction processing.

The back-end unit 226 performs back-end processing of compilation. Namely, the back-end unit 226 reads the optimized intermediate code from the intermediate code storage unit 222 and converts the read intermediate code into an object code. The back-end unit 226 may generates an assembly code written in an assembly language from the intermediate code and convert the assembly code into an object code convert. The back-end unit 226 stores the generated object code in the object code storage unit 223.

FIG. 15 is a flowchart illustrating an example of a procedure of reduction processing.

Hereinafter, processing performed by the thread 123 a started based on the object code generated by the compiling device 200 will be described. The threads 123 b to 123 d are also started based on the same object code and performs the same processing.

(S10) The thread 123 a generates the array 43 a (array sum_k), which is a copy of the array 42 (array sum), in the stack area 121 a that corresponds to the thread 123 a.

(S11) The thread 123 a stores the address of the head of the array 43 a in a row that is included in the pointer array 44 (pointer array adr) in the shared area 122 and that corresponds to the thread 123 a. If the thread ID of the thread 123 a is tid, the row in which the address is stored is the (tid×16+1)th row in the pointer array 44, for example.

(S12) The thread 123 a initializes the array 43 a. If the reduction operator is “+,” the thread 123 a initializes each row in the array 43 a to 0.

(S13) The thread 123 a generates intermediate data and stores the generated intermediate data in the array 43 a. For example, for each of the 1st to 4th rows in the 2D array 41, the thread 123 a aggregates the values in the 1st and 2nd columns, which are handled by the thread 123 a, and stores the sum in the array 43 a.

(S14) In accordance with barrier synchronization, the thread 123 a waits until the threads 123 b to 123 d complete their processing in step S13.

(S15) The thread 123 a selects one of the threads 123 a to 123 d. The thread that has been selected will hereinafter be referred to as a thread #j.

(S16) The thread 123 a reads the address corresponding to the thread #j from the pointer array 44 in the shared area 122. If the thread ID of the thread #j is j, the row from which the address is read is the (j×16+1)th row in the pointer array 44, for example.

(S17) The thread 123 a determines a row in which the thread 123 a aggregates intermediate data in the array 42. The row determined in step S17 will be referred to as a row #i.

(S18) On the basis of the address read in step S16, the thread 123 a reads the intermediate data in the i-th row from the stack area that corresponds to the thread #j. The thread 123 a reflects the read intermediate data in the i-th row (sum(i)) in the array 42 in the shared area 122. If the reduction operator is “+,” the thread 123 a adds the value read from the stack area that corresponds to the thread #j to sum(i).

(S19) The thread 123 a determines whether all the threads 123 a to 123 d have been selected in step S15. If all the threads have been selected, the processing proceeds to step S20. Otherwise, the processing returns to step S15.

(S20) In accordance with barrier synchronization, the thread 123 a waits until the threads 123 b to 123 d complete their processing in steps S15 to S19.

(S21) The thread 123 a allows deletion of the array 43 a from the stack area 121 a. The thread 123 a ends the reduction processing.

FIG. 16 is a flowchart illustrating an example of a procedure of compilation.

(S30) The front-end unit 224 reads a source code from the source code storage unit 221, analyzes the source code, and converts the source code into an intermediate code. The front-end unit 224 stores the intermediate code in the intermediate code storage unit 222. In the following steps S31 to S38, the optimization unit 225 performs processing for parallelization on the intermediate code.

(S31) The optimization unit 225 adds a private variable, which is a copy of the reduction variable specified by the reduction directive, in the intermediate code. Attributes of the private variable such as the data type, array length, and dimension are the same as those of the original reduction variable.

(S32) The optimization unit 225 adds a shared variable indicating a pointer array in the intermediate code. The length of the pointer array is determined based on the maximum number of CPU threads that execute the object code (for example, the number of CPU cores) and the cache line size.

(S33) The optimization unit 225 adds a code for storing the address of the private variable added in step S31 (for example, a physical address in the RAM 102) in the pointer array in the intermediate code. The row in which the address is stored is calculated from the corresponding thread ID.

(S34) The optimization unit 225 adds a code for initializing the private variable added in step S31 in the intermediate code. The initial value of the private variable is determined based on the reduction operator specified in the reduction directive.

(S35) The optimization unit 225 replaces access to the reduction variable included in the intermediate code with access to the private variable added in step S31.

(S36) The optimization unit 225 adds a code for reading the address of each thread stored in the pointer array in the intermediate code.

(S37) The optimization unit 225 adds a code for updating the reduction variable by using the intermediate data stored in the private variables indicated by the addresses in step S36 in the intermediate code. The updating of the reduction variable is performed by using the reduction operator specified.

(S38) The optimization unit 225 adds a code for causing a plurality of threads to perform barrier synchronization immediately before the code in step S36. In addition, the optimization unit 225 adds a code for causing the plurality of threads to perform barrier synchronization immediately after the code in step S37.

(S39) The back-end unit 226 reads the optimized intermediate code from the intermediate code storage unit 222 and converts the intermediate code into an object code. The back-end unit 226 stores the object code in the object code storage unit 223.

In the information processing system according to the third embodiment, the threads 123 a to 123 d are started by the CPU cores 101 a to 101 d, and the intermediate data is separately stored in the stack areas 121 a to 121 d that correspond to the threads 123 a to 123 d, respectively. In addition, the addresses that indicate the locations of the intermediate data are stored in the shared area 122. The threads 123 a to 123 d access the stack areas 121 a to 121 d by referring to the addresses stored in the shared area 122 and aggregate their intermediate data in parallel.

In this way, unlike the above second method in which the intermediate data is stored in the shared area 122, since no area needs to be dynamically allocated in the shared area 122 for the intermediate data in the present embodiment, the overhead, which is caused by the above second method, is not caused in the present embodiment. In addition, unlike the above first method in which the threads reflect their intermediate data in the resultant data in the shared area 122, since exclusive control among the threads 123 a to 123 d is not performed in the present embodiment, the above overhead, which is caused by the first method in which exclusive control is performed, is not caused in the present embodiment. In addition, the intermediate data is aggregated in parallel. In addition, since the threads 123 a to 123 d that have generated the intermediate data aggregate the necessary intermediate data, no new thread is started. Namely, while overhead is caused if a new thread is started, since no new thread is started in the present embodiment, no such overhead is caused in the present embodiment. Thus, the threads 123 a to 123 d are able to perform reduction processing at high speed.

As described above, the information processing according to the first embodiment may be realized by causing the parallel computing device 10 to execute a program. The information processing according to the second embodiment may be realized by causing the compiling device 20 to execute a program. The information processing according to the third embodiment may be realized by causing the parallel computing device 100 and the compiling device 200 to execute a program.

Each of these programs may be recorded in a computer-readable recording medium (for example, the recording medium 113 or 213). As the recording medium, for example, a magnetic disk, an optical disc, a magneto-optical disk, or a semiconductor memory may be used. Examples of the magnetic disk include a FD and an HDD. Examples of the optical disc include a CD, a CD-recordable (R)/rewritable (RW), a DVD, and a DVD-R/RW. The program may be recorded in a portable recording medium and distributed. In this case, after a copy of the program is created from the portable recording medium and the copy is stored in another recording medium such as an HDD (for example, the HDD 103 or 203), the copy is executed.

According to one aspect, a plurality of threads are able to aggregate intermediate data at high speed.

All examples and conditional language provided herein are intended for the pedagogical purposes of aiding the reader in understanding the invention and the concepts contributed by the inventor to further the art, and are not to be construed as limitations to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although one or more embodiments of the present invention have been described in detail, it should be understood that various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention. 

What is claimed is:
 1. A parallel computing apparatus comprising: a first processor configured to execute a first thread; a second processor configured to execute a second thread; and a memory configured to include a first private area that corresponds to the first thread, a second private area that corresponds to the second thread, and a shared area, wherein the first processor stores first data in the first private area and stores address information that enables access to the first data in the shared area, and wherein the second processor stores second data in the second private area, accesses the first data based on the address information stored in the shared area, and generates third data based on the first data and the second data.
 2. The parallel computing apparatus according to claim 1, wherein the first processor synchronizes the first thread and the second thread so that the first data is not deleted from the first private area until at least the second processor accesses the first data.
 3. The parallel computing apparatus according to claim 1, wherein the second processor stores fourth data in the second private area and stores other address information that enables access to the fourth data in the shared area, and wherein the first processor stores fifth data in the first private area, accesses the fourth data based on said other address information stored in the shared area, and generates sixth data based on the fourth data and the fifth data.
 4. The parallel computing apparatus according to claim 3, wherein each of the first and second processors includes a cache memory, and wherein the address information and said other address information is stored separately by a distance based on a cache line size of the cache memory in the shared area.
 5. A compiling apparatus comprising: a memory configured to hold a first code that is to generate first data; and a processor configured to convert the first code into a second code that is to start a first thread for generating second data and a second thread for generating third data and then generating the first data based on the second data and the third data, wherein the second code includes a first instruction that causes the first thread to store the second data in a first private area that corresponds to the first thread and that causes the second thread to store the third data in a second private area that corresponds to the second thread, wherein the second code includes a second instruction that causes the first thread to store address information that enables access to the second data in a shared area, and wherein the second code includes a third instruction that causes the second thread to access the second data based on the address information stored in the shared area.
 6. A parallel processing method comprising: starting, by a first processor, a first thread; starting, by a second processor, a second thread; storing, by the first processor, first data in a first private area that is included in a memory and that corresponds to the first thread and storing address information that enables access to the first data in a shared area included in the memory; storing, by the second processor, second data in a second private area that is included in the memory and that corresponds to the second thread; and accessing, by the second processor, the first data based on the address information stored in the shared area and generating third data based on the first data and the second data. 